Continuous-time convolutions model of event sequences

Massive samples of event sequences data occur in various domains, including e-commerce, healthcare, and finance. There are two main challenges regarding inference of such data: computational and methodological. The amount of available data and the length of event sequences per client are typically large, thus it requires long-term modelling. Moreover, this data is often sparse and non-uniform, making classic approaches for time series processing inapplicable. Existing solutions include recurrent and transformer architectures in such cases. To allow continuous time, the authors introduce specific parametric intensity functions defined at each moment on top of existing models. Due to the parametric nature, these intensities represent only a limited class of event sequences. We propose the COTIC method based on a continuous convolution neural network suitable for non-uniform occurrence of events in time. In COTIC, dilations and multi-layer architecture efficiently handle dependencies between events. Furthermore, the model provides general intensity dynamics in continuous time - including self-excitement encountered in practice. The COTIC model outperforms existing approaches on majority of the considered datasets, producing embeddings for an event sequence that can be used to solve downstream tasks - e.g. predicting next event type and return time. The code of the proposed method can be found in the GitHub repository (https://github.com/VladislavZh/COTIC).